Linear algebraic and linear programming techniques for the analysis of place/transition net systems

Abstract

The structure theory of Place/Transition net systems is surveyed — incorporating new contributions — in a tutorial style, mainly from a linear algebraic perspective. Topics included are: state equation based analysis of safety properties (e.g., boundedness, mutual exclusion, deadlock-freeness, etc.), linear invariants, siphons and traps, implicit places and their application to improve the accuracy of the state equation, and rank theorems (structural conditions for liveness and boundedness based on the rank of the incidence matrix).